A class of fuzzy clusterwise regression models

D’Urso, Pierpaolo; Massari, Riccardo; Santoro, Adriana

doi:10.1016/j.ins.2010.08.018

Cited by 29 publications

(8 citation statements)

References 68 publications

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“…proposed the combined use of multiple correspondence analysis (MCA) (Benzécri 1973;Gifi 1990) and fuzzy c-means clustering in order to extract heterogeneous subgroups of objects, which is called fuzzy cluster MCA (FMCA). In addition, as a generalization of linear cluster-wise regression analysis (Späth 1979), several procedures for fuzzy linear cluster-wise regression have been proposed (Bezdek et al 1981;Wedel and Steenkamp 1989;Hathaway and Bezdek 1993;D'Urso et al 2010). Likewise, some methods in which clustering and another method of multivariate analysis are combined in a single framework have been developed, for example by Rocci and Vichi (2005), Vichi et al (2007), , and Hwang et al (2007).…”

Section: Proposed Method: Fcbamentioning

confidence: 99%

A new biplot procedure with joint classification of objects and variables by fuzzy c-means clustering

Yamashita

Mayekawa

2014

Adv Data Anal Classif

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Biplot is a technique for obtaining a low-dimensional configuration of the data matrix in which both the objects and the variables of the data matrix are jointly represented as points and vectors, respectively. However, biplots with a large number of objects and variables remain difficult to interpret. Therefore, in this research, we propose a new biplot procedure that allows us to interpret a large data matrix. In particular, the objects and variables are classified into a small number of clusters by using fuzzy c-means clustering and the resulting clusters are simultaneously biplotted in lower-dimensional space. This procedure allows us to understand the configurations easily and to grasp the fuzzy memberships of the objects and variables to the clusters. A simulation study and real data example are also provided to demonstrate the effectiveness of the proposed procedure.

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Section: Proposed Method: Fcbamentioning

confidence: 99%

A new biplot procedure with joint classification of objects and variables by fuzzy c-means clustering

Yamashita

Mayekawa

2014

Adv Data Anal Classif

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“…The general form of a fuzzy regression model for crisp/ fuzzy-input data and fuzzy-output data can be expressed as follows (D'Urso and Gastaldi 2000;D'Urso 2003;D'Urso et al 2010;Wang et al 2020;Hesamian and Akbari 2021;Chachi and Chaji 2021; where 1.…”

Section: Fuzzy Regressionmentioning

confidence: 99%

MADM approach to analyse the performance of fuzzy regression models

Kazemifard

Chachi

2021

J Ambient Intell Human Comput

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It is worth to note that estimated parameters of any fuzzy regression model as well as its goodness-of-fit value depend on the objective function being optimized. Thus, it is not easy to compare the solutions of different models that optimize different objective functions. On the other hand, dataset has a significant influence on the performance of any model estimation procedure making the comparison more challengeable. In this paper, we propose a method in order to compare and/or rank a set of fuzzy regression models based on their goodness-of-fit performance analysis when applied to modeling a dataset. With regard to that, the problem of finding the most preferred/desirable model is considered as a multi-attribute decision making (MADM) problem in which the set of candidate models are alternatives and the goodness-of-fit criteria are attributes. Attribute values are calculated based on well-known goodness-of-fit formula while their weights, which are considered as the most important points in MADM problems, are calculated by the entropy measure. Therefore, the entries of the decision matrix are considered as the fitness values of the data points by the models (or alternatives). The entropy values are then transformed to the weight values of the data points illustrating the importance of each data point in the estimation methods of models. Ultimately, the TOPSIS method is employed to provide an algorithm to rank the models. The proposed method not only gives us the rank of the models, but also provides us an index showing how much each ranked model fits the data set.

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“…We also study another version of the generalized CLR problem with the sum of absolute errors as the objective to examine whether the difficulty in solving the pricing problem is due to the nonlinearity of the objective function in the pricing problem (10)- (13). More specifically, we change the objective function in the pricing problem to Figure 9(b) presents the running time when the objective function for the CLR problem is the sum of absolute errors.…”

Section: Time Study Of the Column Generation Algorithmmentioning

confidence: 99%

“…We denote the dual variables of constraints (8) in the master problem by π r , and introduce the binary decision variables z r for r ∈ [R] to indicate whether group G r is selected in the cluster with the minimum reduced cost. To obtain the new pricing problem, we need to replace z i 's with z r 's in the pricing problem (10)- (13). Constraint (13) is changed to R r=1 |G r |z r ≥ n, and the range in constraints (11) and (12)…”

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confidence: 99%

Algorithms for Generalized Clusterwise Linear Regression

Park

Jiang

Klabjan

et al. 2017

INFORMS Journal on Computing

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Cluster-wise linear regression (CLR), a clustering problem intertwined with regression, is to find clusters of entities such that the overall sum of squared errors from regressions performed over these clusters is minimized, where each cluster may have different variances. We generalize the CLR problem by allowing each entity to have more than one observation, and refer to it as generalized CLR. We propose an exact mathematical programming based approach relying on column generation, a column generation based heuristic algorithm that clusters predefined groups of entities, a metaheuristic genetic algorithm with adapted Lloyd's algorithm for K-means clustering, a two-stage approach, and a modified algorithm of Späth [26] for solving generalized CLR. We examine the performance of our algorithms on a stock keeping unit (SKU) clustering problem employed in forecasting halo and cannibalization effects in promotions using real-world retail data from a large supermarket chain. In the SKU clustering problem, the retailer needs to cluster SKUs based on their seasonal effects in response to promotions. The seasonal effects are the results of regressions with predictors being promotion mechanisms and seasonal dummies performed over clusters generated. We compare the performance of all proposed algorithms for the SKU problem with real-world and synthetic data.

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A class of fuzzy clusterwise regression models

Cited by 29 publications

References 68 publications

A new biplot procedure with joint classification of objects and variables by fuzzy c-means clustering

A new biplot procedure with joint classification of objects and variables by fuzzy c-means clustering

MADM approach to analyse the performance of fuzzy regression models

Algorithms for Generalized Clusterwise Linear Regression

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